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Search: id:A098485
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| A098485 |
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Lower triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square array such that their adjacency graph consist of a single component. Two positions (s,t),(u,v) are considered as adjacent, if max(abs(s-u),abs(t-v))<=1. |
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+0
2
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| 1, 4, 6, 9, 20, 48, 16, 42, 132, 419, 25, 72, 256, 973, 3682, 36, 110, 420, 1747, 7484, 31992, 49, 156, 624, 2741, 12562, 58620, 273556, 64, 210, 868, 3955, 18916, 92912, 462104, 2927505, 81, 272, 1152, 5389, 26546, 134868, 697836, 3644935, 19082018
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of ways to mark the numbers on a square board on a lottery play slip such that one connected graphic pattern is formed. For the lottery "mark 6 numbers of 49 on a 7X7 grid of numbers" that is played in many countries, there are T(7,6)=58620 (out of binomial(49,6)=13983816) different combinations of 6 numbers whose graphic pattern on the board forms one connected component.
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LINKS
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John Burkardt, GRAFPACK Graph Computations.
Hugo Pfoertner, Counts of connected components in selected numbers on square lotto boards..
Hugo Pfoertner, Program to analyze the adjacency graph of selections on lotto boards..
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EXAMPLE
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a(5)=T(3,2)=20 because there are 20 ways to mark two positions in a 3 X 3 square grid such that the two picked positions are either row-wise, column-wise or diagonally adjacent:
XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000
000...X00...0X0...000...X00...0X0...00X...0X0...00X...XX0
000...000...000...000...000...000...000...000...000...000
.........................................................
000...000...000...000...000...000...000...000...000...000
000...X00...0X0...000...X00...0X0...00X...0X0...00X...0XX
XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000
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PROGRAM
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FORTRAN program: See link.
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CROSSREFS
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Cf. A090642, binomial(n^2, k), 0<=k<=n; A098487, selections where all marks are isolated from each other.
Sequence in context: A036667 A056016 A152002 this_sequence A120712 A115698 A039566
Adjacent sequences: A098482 A098483 A098484 this_sequence A098486 A098487 A098488
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KEYWORD
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nonn,tabl
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 14 2004
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